DOCUMENTA MATHEMATICA, Vol. 21 (2016), 689-734

Holger Deppe

p-adic L-Functions of Automorphic Forms and Exceptional Zeros

We construct $p$-adic L-functions for automorphic representations of $\GL2$ of a number field $F$ , and show that the corresponding $p$-adic L-function of a modular elliptic curve $E$ over $F$ has an extra zero at the central point for each prime above $p$ at which $E$ has split multiplicative reduction, a part of the exceptional zero conjecture.

2010 Mathematics Subject Classification: 11F41, 11F67, 11F70, 11G40

Keywords and Phrases: p-adic L-function, automorphic forms, exceptional zero conjecture, Mazur-Tate-Teitelbaum conjecture

Full text: dvi.gz 106 k, dvi 329 k, ps.gz 641 k, pdf 529 k.